Enhanced Crystal Quality of Al_xIn_1-xAs_ySb_1-y for Terahertz Quantum Cascade Lasers

Abstract

This work provides a detailed study on the growth of Al_xIn_1-xAs_ySb_1-y lattice-matched to InAs by Molecular Beam Epitaxy. In order to find the conditions which lead to high crystal quality deep within the miscibility gap, Al_xIn_1-xAs_ySb_1-y with x = 0.462 was grown at different growth temperatures as well as As₂ and Sb₂ beam equivalent pressures. The crystal quality of the grown layers was examined by high-resolution X-ray diffraction and atomic force microscopy. It was found that the incorporation of Sb into Al_0.462In_0.538As_ySb_1-y is strongly temperature-dependent and reduced growth temperatures are necessary in order to achieve significant Sb mole fractions in the grown layers. At 480 ${}^{\circ }\mathrm{C}$ lattice matching to InAs could not be achieved. At 410 ${}^{\circ }\mathrm{C}$ lattice matching was possible and high quality films of Al_0.462In_0.538As_ySb_1-y were obtained.

1. Introduction

InAs is an interesting material for inter-subband devices such as quantum cascade lasers (QCLs) due to its low effective mass, since it is expected to enable higher performance by providing higher gain [1]. In order to exploit the beneficial properties of InAs as the well material, a suitable barrier material is necessary. The commonly used Al(As)Sb material, though enabling excellent results for mid-infrared (MIR) devices [2,3,4,5], requires the use of monolayer and sub-monolayer thin barriers for devices designed to emit in the terahertz ($\mathrm{T}\mathrm{Hz}$) regime, due to its very high conduction band offset. The growth of such thin layers is very difficult to control, and to date, no THz laser operation has been shown.

A viable option for the barrier material is the quarternary Al_xIn_1-xAs_ySb_1-y material, which can be grown lattice-matched to InAs and should have properties tunable from InAs to AlAs_0.16Sb_0.84. By choosing an appropriate composition, it would be possible to grow InAs based THz QCLs with a low conduction band offset and therefore easy to control barrier thicknesses.

Reports about the growth of Al_xIn_1-xAs_ySb_1-y at various compositions can be found in literature, however, most of these works do not specifically study the growth of Al_xIn_1-xAs_ySb_1-y and hence little information exists on the effect of the various growth parameters on the crystal quality and layer composition. An overview of the compositions and the respective growth temperatures is given in Figure 1. Turner et al. [6] and Wilk et al. [7] report on the growth Al_xIn_1-xAs_ySb_1-y with Al mole fractions below 0.20 at growth temperatures (T_g) of 430 ${}^{\circ }\mathrm{C}$ and 420 ${}^{\circ }\mathrm{C}$, while Semenov et al. [8] show that compositions with Al mole fractions of up to 0.25 can be grown at a T_g of 450°C to 500${}^{\circ }\mathrm{C}$. For the greatest flexibility when it comes to designing devices employing Al_xIn_1-xAs_ySb_1-y, composition with higher Al mole fractions have to be investigated and conditions have to be found which suit the widest range of compositions. The growth of Al_xIn_1-xAs_ySb_1-y on GaAs with higher Al mole fractions is reported at a T_g well below 400 ${}^{\circ }\mathrm{C}$. Kudo et al. [9] studied the incorporation of Sb into Al_xIn_1-xAs_ySb_1-y with an Al mole fraction of 0.5 at a T_g of 350 ${}^{\circ }\mathrm{C}$ grown on GaAs. The authors report a high dislocation density, found in a transmission electron microscopy study of the grown material, resulting from the highly lattice-mismatched conditions. It is questionable whether this result is applicable to the growth of Al_xIn_1-xAs_ySb_1-y on InAs. Wahsington-Stokes et al. [10] report on the growth of Al_xIn_1-xAs_ySb_1-y with an As mole fraction between 0.37 and 0.72 at a T_g between 355°C and 378${}^{\circ }\mathrm{C}$ on GaSb substrates and report good crystal quality for the grown layers. The influence of the Sb and As beam equivalent pressures (BEP) or the T_g on the quality and composition of the layers is not mentioned.

2. Experiment Section

2.1. Growth Optimization of Al_xIn_1-xAs_ySb_1-y

The lack of information on the growth of Al_xIn_1-xAs_ySb_1-y with Al mole fractions around 0.5 at a T_g above 400 ${}^{\circ }\mathrm{C}$ suggests that challenges, possible due to the presence of a miscibility gap [8], arise from such conditions. Since high crystal quality is expected to be achieved at high T_g, the upper limit for the growth of Al_xIn_1-xAs_ySb_1-y and the dependence of the crystal quality on the T_g have to be investigated.

Al_xIn_1-xAs_ySb_1-y with an aluminum mole fraction fixed to 0.462, was grown on InAs. The growth rates of AlAs (on InAs) (R_AlAs) and InAs (R_InAs) were constant for all samples. R_AlAs was set to 0.25 monolayers per second (MLs⁻¹) which corresponds to an aluminum BEP 1.3 × 10⁻⁷ $\mathrm{torr}$. R_InAs was set to 0.29 MLs⁻¹ equaling an indium BEP of 4.5 × 10⁻⁷ $\mathrm{torr}$. For the comparison of the group V BEPs to other MBE systems, the As₂ flux was calibrated by the (2 × 4) to (4 × 2) transition during growth at different temperatures and normalized to 1 MLs⁻¹. A fit to the exponential function ${\mathrm{P}}_{{\mathrm{As}}_2}\left(T\right)=a+bexp(\frac{T}{c})$ resulted in the parameters $a=0.531\mathrm{torr}$, $b=2.14\times {10}^{-14}\mathrm{torr}$, $c=23.24{\mathrm{K}}^{-1}$. A plot of this experiment can be found in the supplementary material section.

To find the optimum growth conditions, T_g, As₂ BEP (P_As2) and Sb₂ BEP (P_Sb2) were varied. The range of T_g used in this study was 410°C to 480${}^{\circ }\mathrm{C}$. Since Al_xIn_1-xAs_ySb_1-y should be used in heterostructures together with InAs, P_As2 is, in principle, dictated by the optimum BEP to grow high quality InAs [11]. In this study, P_As2 was varied in order to investigate its influence on the composition of Al_0.462In_0.538As_ySb_1-y. The growth parameter regions investigated in this study are indicated by the gray shaded areas in Figure 1.

To investigate the influence of growth parameters, a set of samples was grown in a Riber 32 MBE system on indium-bonded n+ InAs (001) wafers. For the group V materials, valved cracking cells were used with the cracking zone temperatures set to 850°C and 1000${}^{\circ }\mathrm{C}$ to produce As₂ and Sb₂ respectively. For all samples, first the oxide was thermally desorbed under P_As2 of 1.5 × 10⁻⁵ $\mathrm{torr}$ at 510 ${}^{\circ }\mathrm{C}$ for 20 min. The temperature was then reduced to 480 ${}^{\circ }\mathrm{C}$ to grow a 150 $\mathrm{n}\mathrm{m}$ InAs buffer layer to enhance the surface quality after thermal desorption of the oxide. Next, the T_g was adjusted to the desired growth temperature, at which a 150 $\mathrm{n}\mathrm{m}$ thick Al_0.462In_0.538As_ySb_1-y layer and a 5 $\mathrm{n}\mathrm{m}$ InAs cap, were grown.

All fabricated heterostructures were measured with high resolution x-ray diffraction (HRXRD) to investigate the crystal quality and composition. The As mole fraction (y) in the grown Al_0.462In_0.538As_ySb_1-y layers was corroborated by measuring their in-plane and out-of-plane lattice constant in reciprocal space maps around the InAs (224) diffraction peak and applying Vegard’s law. Atomic force microscopy (AFM) was used to determine the surface roughness of all samples.

To investigate the incorporation of Sb into Al_0.462In_0.538As_ySb_1-y, three series of samples were grown. For each series P_As2 and the T_g were kept constant while P_Sb2 was varied. P_As2 was chosen such that high crystal quality InAs can be grown under the same conditions [11]. The results are summarized in Figure 2a. It shows that with increasing P_Sb2, the rate of Sb incorporation is lowered and a maximum achievable Sb mole fraction is approached asymptotically. Only at a T_g of 410 ${}^{\circ }\mathrm{C}$ can lattice matching with InAs achieved. An explanation for this behavior may be found in the As-for-Sb exchange reaction found for other mixed group V materials like GaAsSb [14]. Due to its negative enthalpy, this reaction is favored with respect to the reverse reaction and its rate rises with T_g for experiments using As₂, which is in agreement with our observations.

HRXRD measurements, shown in Figure 2b–d, show high crystal quality for P_Sb2 between 0.5 × 10⁻⁶ torr and 1 × 10⁻⁶ $\mathrm{torr}$ at 410 ${}^{\circ }\mathrm{C}$ as well as 1 × 10⁻⁶ torr and 2.5 × 10⁻⁶ $\mathrm{torr}$ at 445 ${}^{\circ }\mathrm{C}$ T_g. This is indicated by sharp layer peaks and Pendellösung fringes. At lower P_Sb2, the layer peaks are broadened due to partial relaxation resulting from the high lattice mismatch. At 410 ${}^{\circ }\mathrm{C}$, even higher P_Sb2 also leads to peak broadening. The respective (224) reciprocal space map shows partial relaxation. Strong peak broadening due to partial relaxation was also found for all samples grown at 480 ${}^{\circ }\mathrm{C}$.

AFM measurements performed on the same heterostructures, shown in Figure 3, confirm these observations. Layers containing very little Sb show crosshatch patterns, a sign of partial relaxation. When the P_Sb2 is increased to values between 0.5 × 10⁻⁶ torr and 1 × 10⁻⁶ $\mathrm{torr}$ for a T_g of 410 ${}^{\circ }\mathrm{C}$ and 1 × 10⁻⁶ torr and 2.5 × 10⁻⁶ torr at 445 ${}^{\circ }\mathrm{C}$, the surface roughness is dramatically reduced and no sign of crosshatch can be found. At 2.55 × 10⁻⁶ $\mathrm{torr}$ and a T_g of 410 ${}^{\circ }\mathrm{C}$, the measurements show an increased surface roughness. Since these conditions cause a 3-D growth mode it is evident that excess Sb₂ has to be avoided at low T_g in order to achieve high crystal quality.

Although it is convenient to keep P_As2 at a value that is optimal for the growth of the InAs throughout the whole growth, it is possible to change the conditions for each layer, since modern As cracking cells are equipped with valves that allow for the quick change of the flux. It could be beneficial to change P_As2 to a lower value for the growth of Al_xIn_1-xAs_ySb_1-y in order to achieve a lower As mole fraction in the layer and hereby circumvent the restrictions imposed by the growth of InAs. To investigate the influence of P_As2 on the composition of Al_0.462In_0.538As_ySb_1-y, a series of samples was grown in which P_Sb2 (1 × 10⁻⁶ torr and 2.5 × 10⁻⁶ $\mathrm{torr}$) and the growth temperature (T_g = 445 ${}^{\circ }\mathrm{C}$) were kept constant while P_As2 was varied. AFM measurements of these samples are shown in Figure 4. From Figure 5a it can be seen that, as expected, decreasing P_As2 leads to a lower As concentration (y) in the layer. Figure 5b, shows that the P_As2 can only be adjusted within a very small range since too little As₂ leads to a dramatic increase in surface roughness, due a 3-D growth mode (Figure 4c). This behavior is even more pronounced for samples grown at P_Sb2 of 2.5 × 10⁻⁶ $\mathrm{torr}$ (Figure 4a). When P_As2 is decreased below ∼3 × 10⁻⁶ $\mathrm{torr}$ no epitaxial growth is possible, illustrating that there is a lower limit to the P_As2. This was determined by both a vanishing RHEED pattern during growth and the absence of a layer peak in the HRXRD measurement.

To understand its origin, samples showing high roughness but no cross hatch in the AFM analysis have been inspected by scanning electron microscopy (SEM) and energy dispersive X-ray spectroscopy (EDX). The micrographs of these samples are shown in Figure 6. Figure 6a shows the effect of low P_As2 on the surface morphology. The too low As flux on the surface leads to a lower surface mobility of the group III adatoms, breaking the layer-by-layer growth mode and resulting in a rough surface. EDX measurements at different spots of the sample show that the four atom species (Al,In,As,Sb) are equally distributed ($\mathsf{\sigma }<0.5\mathrm{at}.\%$). Figure 6b shows the effect of high P_Sb2 at low T_g. Similar to Figure 6a 3-D growth was found. Since this sample was grown with excess P_As2, group V deficiency can be ruled out as the source. As for the previous sample, the EDX analysis showed that all four atom species are homogeneously distributed ($\mathsf{\sigma }<0.5\mathrm{at}.\%$). Increasing P_Sb2 well beyond lattice-matching seems to limit the diffusion length of the group III elements and promote a 3-D growth mode. For both sample (a) and (b) no signs of phase separation due to immiscibility were found and the 3-D morphology seems to be caused by the III/V BEP ratios. High surface roughness was also found for the sample shown in Figure 6c. Unlike for samples (a) and (b) it seems to be due to crystallites with an octagonal base that are well ordered to the substrate. The EDX measurement on this sample shows that the crystallites are rich in antimony while in the surrounding area the composition is close to that found in the HRXRD study. Al and In are homogeneously distributed across the whole sample. This result suggests that Al_0.462In_0.538As_ySb_1-y decomposes into AlInAs and AlInSb under these conditions.

Using the information gathered in this study, two samples were grown on a Riber C21 MBE system on freestanding n+ InAs (001) wafers at a T_g of 410 ${}^{\circ }\mathrm{C}$. Al mole fractions of 0.25 and 0.53 were chosen and the As₂ BEP was adjusted for high quality InAs. P_Sb2 was then adjusted in order to achieve lattice matching with InAs. For both compositions high-quality material was obtained, again confirmed by HRXRD and AFM measurements.

2.2. Low Temperature Growth of InAs Based Inter-Subband Devices

The experimental data presented in this work show that low T_g is necessary in order to achieve high crystal quality for both, InAs and Al_0.462In_0.538As_ySb_1-y. Growth performed at very low T_g, however, can lead to low device performance due to a deterioration of the optical properties and interface quality of the grown materials. To ensure that the requirement to grow at low T_g does not prevent the realization of inter-subband devices, InAs-based devices using AlAsSb barriers were designed and grown at a T_g of 400 ${}^{\circ }\mathrm{C}$. A quantum cascade detector (QCD) structure with a vertical transition was designed using a semi-classical Monte-Carlo approach. The device was processed into a mesa structure and illuminated through a 45° wedge faced. It showed a peak specific detectivity 2.7 × 10⁷ $\mathrm{c}\mathrm{m}\sqrt{\mathrm{Hz}}/\mathrm{W}$ at 300 $\mathrm{K}$ and a center detection wavelength of 4.84 $\mathsf{\mu }\mathrm{m}$ [15]. Moreover, a THz QCL structure based on a 3-well resonant phonon depletion design was grown. Lasing emission at 3.8 $\mathrm{T}\mathrm{Hz}$ was observed by applying a magnetic field at liquid helium temperature. This is the first report of laser performance in the THz regime for InAs-based structures [16].

3. Discussions

A summary of all samples used in this study that have been grown at T_g = 445 ${}^{\circ }\mathrm{C}$ (a) and 410 ${}^{\circ }\mathrm{C}$ (b) is given in Figure 7. In both cases, a large P_As2/P_Sb2 ratio leads to cross hatch, due to a large lattice mismatch. For a T_g of 445 ${}^{\circ }\mathrm{C}$, a P_As2 below 3.3 × 10⁻⁶ $\mathrm{torr}$ leads to a rough surface. Roughening was also found for samples grown at a T_g of 410 ${}^{\circ }\mathrm{C}$ for the highest P_Sb2 of 2.5 × 10⁻⁶ $\mathrm{torr}$. While partial relaxation was found in the reciprocal space map around the InAs (224), the roughening seems to be mainly caused by the high P_Sb2 since no sign of cross hatch was found in either EDX or AFM measurements. Growing at higher P_Sb2 at a T_g of 445 ${}^{\circ }\mathrm{C}$ results in lower film quality, due to the formation of ordered crystallites with an octagonal base. Since these crystallites were found to be rich in Sb in the EDX analysis, it appears that decomposition, probably due to the miscibility gap of the material occurs under these conditions. A first order approximation, shown as the gray shaded area in Figure 7, was used to locate the region of pressures for which lattice matching can be expected. At a T_g of 445 ${}^{\circ }\mathrm{C}$ this region is close, if not within, the region which leads to decomposition and the formation of Sb rich crystallites. At a T_g of 410 ${}^{\circ }\mathrm{C}$ the region at which lattice matching is expected is far below the region for which the roughening due to high P_Sb2 is observed and the growth of lattice-matched high quality material is easily achieved.

The data presented in this study suggests that a T_g of 445 ${}^{\circ }\mathrm{C}$ is the upper limit for lattice matched growth of Al_0.462In_0.538As_ySb_1-y. For a stable growth and high quality material, however, it is advised to use even lower T_g. This is even more critical if the conditions for high-quality InAs and Al_0.462In_0.538As_ySb_1-y have to be met simultaneously.

4. Conclusions

We investigated the growth of Al_0.462In_0.538As_ySb_1-y. It was shown that the incorporation of Sb into Al_0.462In_0.538As_ySb_1-y is strongly temperature-dependent and that this is determining the upper limit of the T_g for which lattice matching can be achieved. Moreover, it was found that the quality of the grown material is very sensitive to the used P_As2, and that low pressures, which are necessary to achieve lattice matching, dramatically increase the roughness of the grown layer. Moreover, it was found that the growth of compositions close to lattice matching at a T_g of 445 ${}^{\circ }\mathrm{C}$ leads to decomposition of Al_xIn_1-xAs_ySb_1-y into AlInAs and AlInSb and the formation of crystallites which significantly decrease in crystal quality. Below this limit, the requirements for the growth of high quality Al_0.462In_0.538As_ySb_1-y and lattice matched growth can be met simultaneously. At a growth temperature of 410 ${}^{\circ }\mathrm{C}$, high quality Al_0.462In_0.538As_ySb_1-y layers, confirmed by both HRXRD and AFM measurements, were grown. To ensure that growth at low T_g does not prevent the use of this material for inter-subband devices, two InAs based inter-subband structures, a QCD and a THz-QCL, were grown. The QCD showed a peak specific detectivity 2.7 × 10⁷ $\mathrm{c}\mathrm{m}\sqrt{\mathrm{Hz}}/\mathrm{W}$ at 300 $\mathrm{K}$ at a center detection wavelength of 4.84 $\mathsf{\mu }\mathrm{m}$. For the THz-QCL, we were able to show the first lasing emission in the THz regime, at an emission frequency of 3.8 $\mathrm{T}\mathrm{Hz}$, for InAs-based structures.